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The phrase "vital assumption" is correct and usable in written English.
It can be used when referring to a crucial or essential belief or premise that underpins an argument, theory, or analysis. Example: "In our research, we identified a vital assumption that must be validated for our conclusions to hold true."
Exact(2)
The vital assumption of modified second-order model was that a number of surface sites, nR, are used by each adsorbate.
A vital assumption in siRNA-mediated gene silencing is that knockdown of the target gene is exclusive, and without off-target consequences.
Similar(58)
Sometimes, vital assumptions, or even a complete change of approach, are stated only somewhere tucked away between the calculations, or at the very last page.
This is a critical assumption as it plays a vital role in the development of study designs of research focused on stress physiology and statistical analysis of the resulting data [6], [27].
First, because it is in the nature of science that all disciplines are crucially dependent on their ontological assumptions and models, it is vital that such assumptions and models be challenged with alternative conceptions.
The uniqueness assumption is vital for us to prove the main results.
Since linearity is a vital interrupted time-series assumption, we tested all investigated trends for linearity.
Assessment of the assumptions is vital to ensure the results of indirect comparisons are valid and interpreted appropriately.
A critical assessment of the field's working assumptions is vital if it is to make progress in reducing and preventing men's violence against women.
A critical assessment of the field's working assumptions is vital if it is to contribute to the future prevention of men's violence against women.
[James] talks of "cold-blooded assimilations" that "threaten... to undo our soul's vital secrets," and of the "assumption that spiritual value is undone if lowly origin be asserted".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com